Computer tomographic reconstruction with interpolation

ABSTRACT

The invention relates to a computer tomograph having a radiation source from which there issues a beam which has a fan angle and can be moved about a system axis within a measuring field defined by the fan angle in order to scan an object under examination, and having a detector system, which is provided for detecting the radiation issuing from the radiation source and which supplies output signals corresponding to the received radiation, which are fed to an electronic computer. The latter reconstructs on the basis of the output signals images of the object under examination with reference to a reconstruction field which is larger than the measuring field.

[0001] The invention relates to a computer tomograph having a radiation source from which there issues a beam which has a fan angle and can be moved about a system axis within a measuring field defined by the fan angle in order to scan an object under examination, and having a detector system, which is provided for detecting the radiation issuing from the radiation source and which supplies output signals corresponding to the received radiation, an electronic computer reconstructing images of the object under examination from data corresponding to the output signals.

[0002] Computer tomography is an imaging method for producing sectional images that is used principally in the medical field.

[0003] In the case of a computer tomograph of the type mentioned at the beginning that is disclosed in DE 198 35 296 A1, the size of the circular reconstruction field with reference to which images can be reconstructed is limited by the likewise circular measuring field, which is inscribed in the fan angle of the X-ray beam. In order to enlarge the reconstruction field, the fan beam angle and, correspondingly, the detector must be enlarged. This renders it clear that enlarging the reconstruction field leads, in particular, to substantial costs on the detector side.

[0004] It is the object of the invention to design a computer tomograph of the type mentioned at the beginning such that an enlargement of the reconstruction field is possible in a cost-effective way.

[0005] According to the invention, this object is achieved by a computer tomograph having the features of patent claim 1.

[0006] Thus, in the case of the computer tomograph according to the invention the electronic computer reconstructs images, while retaining the fan angle and the detector geometry and on the basis of data corresponding to the output signals of the detector system, with reference to a reconstruction field which is larger than the measuring field inscribed in the fan angle. It is possible in this way to realize an enlarged reconstruction field, and also to represent regions of an object under examination that are located outside the circle inscribed in the fan angle, without the need to enlarge the detector system in conjunction with the extra costs associated therewith. Since the fan angle is not enlarged, the radiation dose (patient dose) fed to the object under examination remains constant, in addition.

[0007] In accordance with a preferred embodiment of the invention, the enlarged reconstruction field is realized by virtue of the fact that the electronic computer obtains the data relating to the region of the reconstruction field lying outside the measuring field by extrapolation starting from data picked up during scanning of the measuring field, if the data relating to the reconstruction of the region of the reconstruction field lying outside the measuring field is not obtained in any case during scanning of the measuring field. Use is made in this case of the circumstance that during scanning of the measuring field there is also a partial scanning of regions of the object under examination that are located outside the measuring field, and it is therefore necessary to obtain by extrapolation only a portion of the data required for the reconstruction of images with reference to the reconstruction field being enlarged. Since it follows therefrom that the data used for the reconstruction of images with reference to the enlarged reconstruction field are obtained only partially by extrapolation, it is clear that it is possible according to the invention to reconstruct images with few artifacts despite the partial extrapolation of data.

[0008] In accordance with a particularly preferred embodiment of the invention, the electronic computer obtains the data relating to the region of the reconstruction field lying outside the measuring field by extrapolation of cut projections, for example by virtue of the fact that the electronic computer detects cut projections and extrapolates the data for detected cut projections relating to the region of the reconstruction field lying outside the measuring field. It is ensured in this way that the extrapolation of data is limited to the extent that is absolutely necessary.—The extrapolation of data in the case of cut projections is, however, known per se from EP 0 030 143 A2.

[0009] The measuring field and the reconstruction field likewise preferably have a circular contour and are arranged concentrically with one another, something which can be achieved, for example, when the beam issues from a focus of the radiation source, for example an X-ray radiation source, which can be moved on a circular track about the system axis.

[0010] An exemplary embodiment of the invention is illustrated in the attached schematic drawings, in which:

[0011]FIG. 1 shows in a way partially resembling a block diagram a schematic of a computer tomograph according to the invention,

[0012]FIG. 2 shows a diagram illustrating the difference between a complete and a cut projection,

[0013]FIG. 3 shows a diagram of the variation in the measured value of a cut projection,

[0014]FIGS. 4 and 5 show the geometry of a computer tomograph with reference to the variation in the measured value of an extended, cut projection,

[0015]FIGS. 6 and 7 show diagrams which illustrate the different approaches to the extrapolation of measurement points in the case of the computer tomograph according to the invention, and

[0016]FIGS. 8 and 9 show two cases of examination in which the computer tomograph according to the invention can be used with particular advantage.

[0017] The X-ray computer tomograph illustrated in FIG. 1 has a measuring unit composed of an X-ray radiation source 1, which emits a fan-shaped X-ray beam 2 with a fan angle α, and a detector 3, which is assembled one or more rows of individual detectors, for example in each case 512 individual detectors, arranged sequentially in the direction of the system axis. The focus of the X-ray radiation source 1, from which the X-ray beam 2 issues, is denoted by 4. The object 5 under examination, a human patient in the case of the exemplary embodiment illustrated, lies on a bearing table 6 which extends through the measuring opening 7 of a gantry 8.

[0018] The X-ray radiation source 1 and the detector 3 are fitted opposite one another on the gantry 8. The gantry 8 is mounted such that it can rotate about the z- or system axis, denoted by z, of the computer tomograph, and is rotated about the z-axis in order to scan the object 5 under examination in the (Φ-direction, specifically by an angle which is at least equal to 180° plus the fan angle α. In this case, the X-ray beam 2, which issues from the focus 4, moved on a circularly curved focal track 15, of the X-ray radiation source 1 operated by means of a generator device 9, covers a measuring field 10 of circular cross section. Projections are recorded for predetermined angular positions of the measuring unit 1, 3, what are termed projection angles, the data corresponding to the associated output signals of the detector 3 passing from the detector 3 to an electronic computer 11 which reconstructs from the data corresponding to the projections the attenuation coefficients of the pixels of a pixel matrix and reproduces the latter pictorially on a display unit 12 on which images of the transirradiated layers of the object 5 under examination therefore appear. By way of example, a complete projection is denoted in FIG. 2 by p_(full) and a cut projection by p_(cut).

[0019] Each projection p(l, k) is assigned to a specific angular position in the (Φ-direction, that is to say a projection angle 1 and comprises a number, corresponding to the number of the detector elements, what is termed the channel number N_(S), of measurement points to which in each case the corresponding measured value is assigned, the channel index k=0(1)(N_(S)−1) specifying from which of the detector elements a measured value originates.

[0020] Since the detector 3 can also have a plurality of rows of detector elements, it is possible, if necessary, simultaneously to record a plurality of layers of the object 5 under examination, the number of projections corresponding to the number of the active rows of detector elements then being recorded per projection angle.

[0021] Moreover, what are termed spiral scans can be carried out when the drive 13 assigned to the gantry 8 is suitable for continuously rotating the gantry and, furthermore, a further drive is provided which permits a relative displacement of the bearing table 6, and thus of the object 5 under examination, on the one hand, and of the gantry 8 with the measuring unit 1, 3, on the other hand, in the z-direction.

[0022] In situations in which, as illustrated in FIG. 1, the object 5 under examination has dimensions such that it exceeds the measuring field 10, it is not possible in the case of conventional computer tomographs to reconstruct images free from artifacts without special measures, since, as may be seen from FIG. 2, at least some of the projections are not what are termed complete projections, that is to say ones which cover the entirety of the object 5 under examination, but what are termed cut projections in which the measuring field is exceeded because they do not cover regions of the object 5 under examination that lie outside the measuring field 10. By way of example, a complete projection is denoted in FIG. 2 by p_(full) and a cut projection by p_(cut).

[0023]FIG. 3 shows with a continuous line the typical variation in the measured values of a cut projection p_(cut), the measured value M being plotted against the channel index k. The projection comprises N_(S) measured channels with the channel indices k=0, 1, 2, . . . N_(S)−1. The channel number N_(S) corresponds to the diameter D_(M) of the measuring field 10 entered in FIG. 4.

[0024] As already mentioned, in the case of the use of conventional image-reconstruction methods, cut projections cause pronounced image artifacts which strongly impair the representation of the object 5 under examination even within the measuring field 10. Moreover, regions of the object 5 under examination that are located outside the measuring field 10 remain excluded from the reconstruction.

[0025] In the case of the computer tomograph according to the invention, cut projections are detected by the electronic computer 11 in a way to be described in yet more detail below.

[0026] Moreover, in the way to be seen from FIG. 3, the electronic computer 11 extends at least the detected cut projections p(l, k) to produce what are termed extended projections p_(ext)(l, k′) by respectively adding a number of channels N_(ext) symmetrically at the start and end of a projection such that an extended projection has the extended channel number N_(E), of which the channel indices k=0, 1, 2, . . . (N_(S)+2N_(ext)−1).

[0027] The extended channel number N_(E) corresponds to an extended measuring field D_(E), which is entered in FIG. 4.

[0028] The measured values belonging to the channels additionally included in an extended projection P_(ext)(l,k′) are obtained by the electronic computer 11 by extrapolation in a way to be described in yet more detail below, if the respective projection is a cut projection detected by the electronic computer 11. By contrast, the electronic computer 11 sets the measured values belonging to the channels additionally included in an extended projection to zero when the respective projection is a complete projection.

[0029] Thus, in addition to the data referring to the measuring field D_(M) that are present in any case, the electronic computer 11 generates data for an extended measuring field, entered in FIG. 4, of diameter D_(E).

[0030] The extrapolated data, an extended projection including the extrapolated data being illustrated in FIG. 5, are used by the electronic computer 11 in the case of the computer tomograph according to the invention in order to reconstruct images of the object 5 under examination in a reconstruction field, illustrated in FIG. 4, of diameter D_(R)>D_(M), the reconstructed channel number N_(R) corresponding to the reconstruction field D_(R), and it holding that N_(R)<(N_(S)+2N_(ext)).

[0031] However, as is illustrated in FIG. 5, in the interests of a good image quality in the region of the edge of the measuring field, it should be that (N_(S)+2N_(ext))>N_(R).

[0032] In the case of the exemplary embodiment described, it holds that (N_(S)+2N_(ext))=1.2·N_(S), that is to say D_(E)=1.2·D_(M), and N_(R)=1.1·N_(S), that is to say D_(R)=1.1·D_(M).

[0033] Owing to the extrapolation, the data referring to the region, located outside the measuring field, of the reconstruction field or of the extended measuring field are merely estimated values. The latter will occasionally deviate from the data which would be measured with the aid of a real detector, and this leads to falsifications in the reconstructed image. As already explained, the reconstruction of a pixel outside the measuring field is based, however, not only on the data obtained by extrapolation. Rather, as may be seen from FIG. 2, even parts of the object 5 under examination that lie outside the measuring field are covered by the beam in a large number of in part complete and in part cut projections, and thereby contribute to the data corresponding to these projections. This makes plain that the contribution of the data obtained by extrapolation is limited to an image reconstructed by the reconstruction field, such that the object under examination is imaged largely without falsification.

[0034] In details, the electronic computer proceeds as follows in extending projections, detecting cut projection and extrapolating:

[0035] An interval, illustrated in FIG. 3, of N_(th,sco) measurement points is investigated at the start and end of the respective projection in order to detect cut projections. If the mean value M_(A)(1) or M_(E)(1) in accordance with equations (1a) and (1b) of the first or last N_(th,sco) measurement points lies above a predefined threshold value S_(th,sco), it is assumed that a cut projection is present: $\begin{matrix} {{M_{A}(1)} = {\frac{1}{N_{{th},{sco}}} \cdot {\sum\limits_{k = 0}^{N_{{th},{sco}} - 1}{p\left( {l,k} \right)}}}} & \text{(1a)} \\ {{M_{E}(1)} = {\frac{1}{N_{{th},{sco}}} \cdot {\sum\limits_{k = 0}^{N_{{th},{sco}} - 1}{p\left( {l,{N_{S} - 1 - k}} \right)}}}} & \text{(1b)} \end{matrix}$

[0036] A sensible choice of parameter for N_(th,sco) is N_(S)/150, for example. For example, the attenuation value of approximately 5 mm H₂O can be used for S_(th,sco).

[0037] The channels relating to the extended measuring field, of the projections extended at the start and end initially include the measured value zero as is illustrated by dots in FIG. 3. Equation (2) yields the extended projection P_(ext)(l, k′) with channel indices k′=0(1)(N_(S)+2N_(ext)−1): $\begin{matrix} {{p_{ext}\left( {l,k^{\prime}} \right)} = \left\{ \begin{matrix} 0 & , & {\quad {k^{\prime} = {0(1)\left( {N_{ext} - 1} \right)}}} \\ {p\left( {l,{k^{\prime} - N_{ext}}} \right)} & , & {\quad {k^{\prime} = {{N_{ext}(1)}\left( {N_{S} + N_{ext} - 1} \right)}}} \\ 0 & , & {\quad {k^{\prime} = {\left( {N_{S} + N_{ext}} \right)(1)\left( {N_{S} + {2N_{ext}} - 1} \right)}}} \end{matrix} \right.} & (2) \end{matrix}$

[0038] The suitable selection of the extension parameter N_(ext) will be explained in more detail later.

[0039] In the following step, the “measured values” of the “measurement point” to be added to the detected cut projections are determined by extrapolation for the cut projections detected in the previously described way. Although these are not actually measured data, measurement points and measured values will be spoken of below, nevertheless.

[0040] The extrapolation of the measurement points must ensure a uniform transition of the corresponding measured values to zero. FIG. 2 shows for this purpose the relationships, in principle, for an extrapolation within the intervals at the start and end of a projection with N_(ext) measurement points.

[0041] A first simple possibility of extrapolation consists in a linear fit, illustrated in FIG. 6, to the first and last measurement points of the projection in the interval k′ε[N_(ext)(1)(N_(ext)+N_(fit)−1)] or k′ε[(N_(ext)+N_(S)−N_(fit))(1) (N_(ext)+N_(S)−1)] are realized. The extrapolated regions are calculated with the aid of the coefficients c_(0,A), c_(1,A) or c_(0,E), c_(1,E) in accordance with equations (3a) and (3b): on whether l or 1 in the equations

{tilde over (p)} _(ext)(l, k′)=c _(0,A)(l)+c _(1,A)(l)·k′, k′=0(l)(N _(ext)−1)  (3a)

{tilde over (p)} _(ext)(l ,k′)=c _(0,E)(l)+c _(1,E)(l)·k′, k′=(N _(S) +N _(ext))(1)(N _(S)+2N _(ext)−1)  (3b)

[0042] The coefficients can be calculated by means of determining the minimum sum of the quadratic deviations. A simpler alternative is to calculate the mean value of the measurement points in the window of width N_(fit) at the ends of the projection. Together with the first and last valid measurement point, the mean values then determine the coefficients for the linear fit.

[0043] A fit of higher order (for example parabolic fit) of the N_(fit) measurement points k′ε[N_(ext)(1)(N_(ext)+N_(fit)−1)] at the start of the projection and the measurement points k′ε[(N_(ext)+N_(S)−N_(fit))(1)(N_(ext)+N_(S)−1)] at the end of the projection can also be carried out by analogy with the linear fit described. The extrapolation equations (4a) and (4b):

{tilde over (p)} _(ext)(l ,k′)= c _(0,A)(l)+c _(1,A)(l)·k′+c _(2,A)(l)·(k′)² , k′=0(1)(N _(ext)−1)  (4a)

{tilde over (p)} _(ext)(l, k′)= c _(0,E)(l)+c _(1,E)(l)·k′+c _(2,E)(l)·(k′) ² , k′=(N _(S) +N _(ext))(1)(N _(S)+2N _(ext)−1)  (4b)

[0044] hold for a parabolic fit, considered here by way of example.

[0045] The coefficients can be calculated, in turn, by means of determining the minimum sum of the quadratic deviations, or by calculating the mean values within in each case two windows with N_(fit) measurement points at the ends of the projection. The parabolic coefficients are then yielded from the mean values and the first and last valid measurement point of the projection.

[0046] A particularly preferred type of extrapolation is the symmetrical extrapolation illustrated in FIG. 7.

[0047] In this approach, the valid measurement points at the start and end of the projection are copied by reflection at the first and last measurement point of the projection as a continuation of the measured projection into the extrapolation interval. Equations (5a) and (5b) describe the extrapolation rule of this approach, which is distinguished by a very low computational outlay. Equation (5a) relates to the start of the projection, and equation (5b) to the end of the projection:

{tilde over (p)} _(ext)(l,N _(ext) −k)=2S _(A)(l)−p(l ,k) , k=1(1)K _(S,A)  (5a)

{tilde over (p)} _(ext)(1,2N _(S) +N _(ext)−2−k)=2S _(E)(l)−p(l, k), k=(N _(S)−2)(−1)K _(S,E)  (5b)

[0048] In this case, S_(A) and S_(E) are the values of the first and last, respectively, valid measurement point of the projection p(k) considered, with S_(A)=p(0), S_(E)=p(N_(S)−1). K_(S,A) and K_(S,E) are the indices of the first and last measurement points which, with p(K_(S,A))>2S_(A) and p(K_(S,E))>2S_(E), respectively, overshoot the threshold values 2S_(A) and 2S_(E), respectively. The “threshold indices” must in this case be limited to K_(S,A)≦N_(ext) or K_(S,E)N_(S)−N_(ext)−1. It may be pointed out once again that FIG. 7 illustrates the extrapolation, given by equations (5a) and (5b), with measurement point mirroring, it being plain that mirroring is firstly performed at a straight line running through the first and last measured measurement point parallel to the axis, corresponding to the measured value, of the rectangular coordinate system of FIG. 7, and then at a straight line running parallel to the axis corresponding to the channel index k or k′ through the first and last measured measurement point.

[0049] By contrast with the two other approaches described, the approach of symmetrical extrapolation has the advantage of a steady transition at the ends of the projection. Moreover, the noise response of the projection is maintained in the extrapolation interval.

[0050] In order to ensure uniform transitions of the extrapolated measurement points to zero, the extrapolation intervals are also weighted in accordance with equations (6a) and (6b) with the aid of attenuation factors w_(A)(k′) and w_(E)(k′) respectively. It holds in this case for the attenuation factors w_(A)(0)=0, w_(A)(N_(ext)−1)=1, w_(E)(N_(S)+2N_(ext)−1)=0 and w_(E)(N_(S)+N_(ext)−1)=1 that:

p _(ext)(l, k′)={tilde over (p)} _(ext)(l, k′)·w _(A)(k′), k′=0(1)(N _(ext)−1)  ( 6a)

p _(ext)(l, k′)={tilde over (p)} _(ext)(l, k′)·w _(E)(k′) , k=(N _(S) +N _(ext))(1)(N _(S)+2N _(ext)−1)  (6b)

[0051] It is possible, for example, to use cosinusoidal functions in accordance with equations (7a) and (7b) for w_(A)(k′) and w_(E)(k′), respectively: $\begin{matrix} {{w_{A}\left( k^{\prime} \right)} = \left( {\sin {k^{\prime} \cdot \frac{\pi}{2\left( {N_{ext} - 1} \right)}}} \right)^{\tau_{\cos}}} & \text{(7a)} \\ {{w_{E}\left( k^{\prime} \right)} = \left( {{\cos \left( {k^{\prime} - N_{S} - N_{ext}} \right)} \cdot \frac{\pi}{2\left( {N_{ext} - 1} \right)}} \right)^{\tau_{\cos}}} & \text{(7b)} \end{matrix}$

[0052] The cosinusoidal attenuation vectors can be calculated in advance and stored for prescribed extrapolation parameters. The parameter τ_(cos) is selected, for example, in an interval τ_(cos)ε[0.5;3].

[0053] In the interests of optimum image quality for the object under examination with strongly variable structures at the edge of the measuring field (for example shoulder, skull), it is expedient to estimate the extent, present in the cut projections, to which the object under examination exceeds the measuring field in a projection under consideration for the purpose of subsequently adapting the extrapolation parameters for the extrapolation of this projection. It is possible in this case, for example, to vary the parameters N_(ext) and τ_(cos), or else the range of the attenuation factors w_(A) and w_(E), respectively, as a function of a suitable measure of the extent to which the measuring field is exceeded, and of the object structure at the two edges of the projection. In the case of the exemplary embodiment described, use is made as the measure of the ratio of the measured value and the edge of the projection to the maximum measured value of the projection, and of the number of the channels in the intervals [0;K_(S,A)] and [K_(S,E);N_(S)−1].

[0054] The sequences of measurement points in the electronic computer 11 that represent the projections run through a chain of a plurality of processing steps during the image reconstruction. The last step in the chain of the direct calculation of the CT image, for example by back projection, is the filtering of the projections with the aid of a convolution core of high-pass type. In the case of the occurrence of cut projections, this is the cause of the artifacts which occur. It is true that in the case of the invention the extrapolation can be performed basically at any time before the convolution in the reconstruction chain. However, in the case of the exemplary embodiment described, the extrapolation does not take place until as late as possible, that is to say directly before the convolution, in order not to increase unnecessarily the data volume to be processed, and thus the computational outlay, in the preceding steps.

[0055] Filtering with the aid of the convolution core requires projections of length N_(S) to be brought to the convolution length L_(F)≧2N_(S)−1 (convolution-length limit) by adding measurement points with the value zero in order to avoid aliasing errors. L_(F)≧2(N_(S)+2N_(ext))−1 must then hold for the convolution length as regards the projections extended by extrapolation. In general, projections are filtered by multiplication of the discrete spectra in the frequency domain. The discrete projection spectra are calculated as “Fast Fourier Transforms” (FFTs) of length L_(FFT). In this case, for example in the use of what is termed the Radix2-FFT, L_(FFT) must satisfy the equation L_(FFT)=2^(cell(1d(2NS−1))) (1d(x)=logarithm to the base of numeral two of x, ceil(x)=x rounded up to the next larger whole number). If the channel number N_(S) of the projections does not correspond to the power of two, projections can be extrapolated in the “difference interval” without causing an enlargement of the FFT length, and thus increasing the computational outlay. The limitation of the extrapolation range, described by N_(ext), is given by equation (8): $\begin{matrix} {N_{ext} = {\frac{1}{2} \cdot \left( {\frac{L_{FFT}}{2} - N_{S}} \right)}} & (8) \end{matrix}$

[0056] If the channel number of a projection exceeds the convolution-length limit, the filtering causes aliasing errors in the edge region of the projections. Typically, such aliasing errors in the reconstructed images are expressed as a decrease in the CT value level toward the edge of the measuring field. Should the channel number of the projections under consideration be very close to a power of two, the extrapolation step possibly requires violation of the convolution-length limit with 2(N_(S)+2N_(ext))−1>L_(F). Since cut projections lead to an increase in the CT value in the outer region of the measuring field, the opposite effect of the aliasing can be utilized for the purpose of partial compensation. Given a suitable selection of the extrapolation interval, represented by N_(ext), and a moderate level of exceeding the convolution-length limit, an excellent image quality is achieved at the edge of the measuring field. Artifacts caused by cut projections are eliminated, whereas aliasing artifacts do not appear. It is therefore possible to avoid an increase in the convolution length L_(F) and thus in the increased computational outlay connected therewith.

[0057] The extrapolation methods described are to be understood by way of example; other approaches are possible within the scope of the invention. However, the approaches described are regarded as particularly advantageous in relation to the computational outlay to be made, and to the achievable image quality.

[0058] The functionality of the invention is to be demonstrated below with the aid of two exemplary embodiments having high requirements:

[0059] As an example, FIG. 8 shows an examination of the shoulder region of a human patient, whose scapula 16 are located partially outside the measuring field. This inhomogeneous structure at the edge region of the measuring field entails certain inaccuracies in the estimation of the data in the cut projections. Because of the generally elliptical form of the shoulder region, however, it is to be expected at the same time that the measuring field will be exceeded only in the region of the scapulae. In a way similar to that illustrated in FIG. 3, the proportion of the data that are obtained by extrapolation and contribute in the image reconstruction to the image region lying outside the measuring field is limited to a few projections. In a majority of the projections, the object part lying outside the measuring field is within the regular radiation fan and therefore supplies correct contributions to the measured data. Taking the two aspects into consideration, it is therefore possible to assume that the object is reproduced in a largely faithful fashion outside the measuring field.

[0060]FIG. 9 illustrates an examination in the abdominal region of a patient which exceeds the measuring field over the entire extent thereof. The contribution of extrapolated data to image reconstruction is thus considerable. However, as a rule there are no inhomogeneous structures present in the edge region of the measuring field in this anatomical region, but at least a substantially homogeneous tissue 17, and so the extrapolation algorithm can supply a very good approximation of the data. Consequently, in this extreme case, as well, a correct reconstruction of the object is also to be expected outside the measuring field.

[0061] In the case of the exemplary embodiment described, the extrapolation takes place directly upstream of the filtering of the projections with the aid of the convolution core. However, it is also possible within the scope of the invention to undertake the extrapolation at a different point of the processing chain.

[0062] The exemplary embodiment described relates to the medical application of the method according to the invention by using CT technology. However, this can also be applied in the case of other tomographic imaging methods, as well as in the nonmedical field.

[0063] In the case of the abovedescribed exemplary embodiment, the invention is described for fan-beam geometry, that is to say a projection is composed of a number of beams issuing from the respective focal position that corresponds to the channel number. However, the invention can also be applied in the case of parallel beam geometry. In this case, a projection is composed of a number of parallel beams that corresponds to the channel number, the middle one of which beams issues from the respective focal position. Projection in parallel-beam geometry are obtained from projection in fan-beam geometry by the inherently known computing operation that is termed rebinning.

[0064] In the case of the exemplary embodiment described, the relative movement between the measuring unit 1, 3 and the bearing table 6 is produced by the displacement of the bearing table 6. However, it is also possible within the scope of the invention to leave the bearing table 6 fixed and to displace the measuring unit 1, 3 instead. Moreover, it is possible within the scope of the invention to produce the required relative movement by displacing both the measuring unit 1, 3 and the bearing table 6.

[0065] The abovedescribed exemplary embodiment is a 3rd generation computer tomograph, that is to say the X-ray radiation source and the detector system are placed jointly about the system axis during the image generation.

[0066] However, the invention can also be applied in conjunction with 4th generation CT units in the case of which only the X-ray radiation source is placed about the system axis and cooperates with a fixed detector ring, provided that the detector system is a planar array of detector elements.

[0067] It is also possible in the case of 5th generation CT units, that is to say CT units where the X-ray radiation issues not only from one focus, but from a plurality of foci of one or more X-ray radiation sources displaced about the system axis, for the method according to the invention to be used, provided that the detector system has a planar array of detector elements.

[0068] The abovedescribed computer tomograph has a detector system with detector elements arranged in the manner of an orthogonal matrix. However, the invention can also be used in conjunction with a detector system that has detector elements arranged in another way other than a planar array, or in the form of a single row. 

1. A computer tomograph having a radiation source from which there issues a beam which has a fan angle and can be moved about a system axis within a measuring field defined by the fan angle in order to scan an object under examination, and having a detector system, which is provided for detecting the radiation issuing from the radiation source and which supplies output signals corresponding to the received radiation, an electronic computer reconstructing from data corresponding to the output signals images of the object under examination with reference to a reconstruction field which is larger than the measuring field.
 2. The computer tomograph as claimed in claim 1, in which the electronic computer obtains the data relating to the region of the reconstruction field lying outside the measuring field by extrapolation starting from data picked up during scanning of the measuring field.
 3. The computer tomograph as claimed in claim 2, in which the electronic computer obtains the data relating to the region of the reconstruction field lying outside the measuring field by extrapolation of cut projections.
 4. The computer tomograph as claimed in claim 3, in which the electronic computer detects cut projections and extrapolates the data for detected cut projections relating to the region of the reconstruction field lying outside the measuring field.
 5. The computer tomograph as claimed in one of claims 1 to 4, in which the measuring field and the reconstruction field have a circular contour and are arranged concentrically with one another.
 6. The computer tomograph as claimed in claim 5, the beam of which issues from a focus of the radiation source that can be moved on a circular track about the system axis.
 7. The computer tomograph as claimed in one of claims 1 to 6, which has as radiation source an X-ray radiation source issuing X-ray radiation. 